If you're in Mumbai for the first time, you can go ahead and look at the main attractions first, like the Gateway of India, Sanjay Gandhi National Park, Marine Drive, Sea link etc. Stay in a centrally located hotel, and go ahead and explore. You shouldn't miss out on some great food while you're there.
You can see this blog for some guidance on food while you're in Mumbai - www.holidify.com/blog/mumbai-street-food/
For other queries, and to sort out your travel plan, visit - www.holidify.com/mumbai